# Math Help - Poisson distribution help

1. ## Poisson distribution help

Question is :

5. Write down the probability distribution of a Poisson random variable with
parameter $\mu$
The average number of earthquakes in a certain region is 2 per week. Assume
that, in any time interval, the number of earthquakes occurring has a Poisson
distribution, calculate
(i) the probability of no earthquakes in a given week;
(ii) the probability of at least 1 earthquake in a given week;
(iii) the probability of at least 3 earthquakes in a given fortnight.
(iv) Calculate the probability that the time until the next earthquake, starting from now, is at least 1 week.

I need help on part (iv) my answers for the others parts are :

i) P(x=o) (e^-2 x 2^0)/0! =0.1353
ii) $P(x\geq1) =1-P(x\leq0)
1-0.1353=0.8647$

iii) $P(x\geq3)=1-P(x\leq2)$
$p(x\leq2)=P(x=0)+p(x=1)+p(x=2) =
1-P(x\leq2)=0.3233$

thanks

2. Originally Posted by master_2m8
Question is :

5. Write down the probability distribution of a Poisson random variable with
parameter $\mu$
The average number of earthquakes in a certain region is 2 per week. Assume
that, in any time interval, the number of earthquakes occurring has a Poisson
distribution, calculate
(i) the probability of no earthquakes in a given week;
(ii) the probability of at least 1 earthquake in a given week;
(iii) the probability of at least 3 earthquakes in a given fortnight.
(iv) Calculate the probability that the time until the next earthquake, starting from now, is at least 1 week.

I need help on part (iv) my answers for the others parts are :

i) P(x=o) (e^-2 x 2^0)/0! =0.1353
ii) $P(x\geq1) =1-P(x\leq 0)
\Rightarrow 1-0.1353 =0.8647$

iii) $P(x\geq3)=1-P(x\leq2)$
$p(x\leq2)=P(x=0)+p(x=1)+p(x=2) =
1-P(x\leq2)=0.3233$